The following R code computes the relative importance for predictor variables in a survival model. The implemented method for computing the relative importance was inspired by the Leo Breiman’s method for computing variable importance in a Random Forest.

Breiman’s method for computing variable importance can best be explained with an example.

Suppose you have 5 predictor variables, say *x*_{1} to *x*_{5}. These 5 variables are used for predicting some observed response *y*. However, the 5 variables do not predict exactly the observed values for *y*. In other words, the predictions based on the 5 variables will more or less deviate from the observed values for *y*. The Mean Squared Error (MSE) is calculated as the mean of these deviations.

Assume now that predictor *x*_{1} has no predictive value for the response *y*. Hence, if we would randomly permute the observed values for *x*_{1}, then our predictions for *y* would hardly change. As a consequence, the MSE before and after permuting the observed values for *x*_{1} would be similar.

On the other hand, assume that *x*_{3} is strongly related to our response *y*. If we randomly permute the observed values for *x*_{3}, then our MSE before and after this permutation would deviate considerably.

Based on these random permutations and our observed change in MSE, we may conclude that predictor variable *x*_{3} is more important than *x*_{1} in predicting *y*.

The R code below applies Breiman’s permutation method for computing the relative importance of predictor variables to a survival model. However, instead of MSE the code employs concordance as a measure for the prediction accuracy.

Furthermore, the R code also compares in 2 simulations the performance of Breiman’s method applied to survival models with that of Breiman’s method implemented in a random survival forest.

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